In a performance audit of 200 public health centers across a administrative division, adop… — State PSC Exam

In a performance audit of $200$ public health centers across a administrative division, adoption of three digital portals was evaluated: Tele-consultation ( $T$ ), Electronic Health Records ( $E$ ), and Medicine Inventory Management ( $M$ ). The audit revealed the following findings:

- $105$ centers use Tele-consultation ( $T$ )
- $90$ centers use Electronic Health Records ( $E$ )
- $85$ centers use Medicine Inventory Management ( $M$ )
- $40$ centers use both $T$ and $E$
- $35$ centers use both $E$ and $M$
- $30$ centers use both $T$ and $M$
- $15$ centers use all three platforms

How many public health centers utilize exactly two of the three digital health platforms?

60Cevap
B
105
C
90
D
45

Cevap

60 public health centers utilize exactly two of the three digital health platforms.

The number of centers using 'exactly two' platforms consists of three distinct regions: (Centers in

T

and

E

only) + (Centers in

E

and

M

only) + (Centers in

T

and

M

only). Since each given pairwise intersection includes the 15 centers that use all three portals, we subtract 15 from each pairwise value:

(40 - 15) + (35 - 15) + (30 - 15) = 25 + 20 + 15 = 60

Adım Adım Çözüm

Identify given set cardinalities and intersections

Total universe

N = 200

;

n(T \cap E) = 40

n(E \cap M) = 35

n(T \cap M) = 30

, and

n(T \cap E \cap M) = 15

The given pairwise intersections include centers that use all three platforms.

Calculate centers using strictly two platforms (excluding the triple overlap)

Centers using ONLY

T

and

E = 40 - 15 = 25

.
Centers using ONLY

E

and

M = 35 - 15 = 20

.
Centers using ONLY

T

and

M = 30 - 15 = 15

To find 'exactly two', centers using all three must be removed from each pairwise intersection.

Sum the exclusive two-set regions

Total =

25 + 20 + 15 = 60

Adding these mutually exclusive regions yields the exact total of centers using exactly two portals.

Anahtar Kavram

3-Set Venn Diagram Region Isolation (Inclusion-Exclusion Principle)

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

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